About the Cauchy problem for nonlinear system with conformable derivatives and variable delays

In the paper are made some notes to the newly introduced conformable derivative as a type local fractional derivative and it is presented a surprising result about the relation between the conformable derivatives and the usual integer order derivatives. As a consequence is considered an initial problem for system of nonlinear differential equations with conformable derivatives and delays. A scheme is shown how to transform it to equivalent well studied initial problem for system of integer first order equations with delays and as standard also to an system of Volterra integral equations, even in the case when the lower terminal of the conformable derivatives coincides with the right side of the initial interval. For convenience such transforms are made first for an initial value problem for nonlinear differential equation with conformable derivative without delay and with initial condition at the lower terminal of the derivative.